How to Correctly Integrate S(x(x+1)^(1/2)) dx?

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Homework Help Overview

The discussion revolves around the integration of the function S(x(x+1)^(1/2)) dx, focusing on the steps and transformations involved in the integration process.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use substitution with u=x+1 and expresses the integral in terms of u. Some participants point out errors in the simplification steps taken during the integration process. Others suggest verifying the final expression against the original form of the question.

Discussion Status

Participants are actively engaging with the original poster's attempts, providing corrections and suggestions for reformatting the final answer. There is a collaborative effort to clarify the integration steps without reaching a definitive conclusion.

Contextual Notes

There is an indication that the online homework system has marked the original poster's solution as incorrect, prompting further examination of the steps taken. Participants are also discussing the importance of expressing the final answer in a specific format.

tjohn101
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Homework Statement


S(x(x+1)1/2) dx

Homework Equations


The Attempt at a Solution


u=x+1
du=1
x=u-1

S(x(u)1/2) du

S(((u-1)(u)1/2) du

S((u2-u)1/2) du

S(u-u1/2) du

S((1/2)u2-(2/3)u3/2)

=(1/2)(x+1)2-(2/3)(x+1)3/2) + COnline homework says it's wrong... Where did I mess up?
 
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Hi tjohn101! :smile:

(have an integral: ∫ :wink:)
tjohn101 said:
S(((u-1)(u)1/2) du

S((u2-u)1/2) du

S(u-u1/2) du

Neither of these lines is correct. :redface:

(u-1)√u = u√u - √u :wink:
 
Ahhhh thank you. I didn't notice I had done that :/
 
Hmmm I ended up getting

(2/5)(x+1)5/2-(2/3)(x+1)3/2 + C

Sound right?
 
Hi tjohn101! :smile:

(just got up :zzz: …)

Yes :smile:but perhaps you should put it in the same form as the question, ie √(x+1) times an ordinary polynomial in x ? :wink:
 
Thank you for your help!
 

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